Simple angle rules

Learning Objective:

• we are learning to find:
  • angles at a point
  • angles at a point on a straight line
  • angles in an X shape (vertically opposite angles)

Investing:

• This is useful because we need to find angles in lots of everyday contexts: bearings, designing and making including arctitecture, engineering and science
• A functional (real-life) application is if you know the bearing you took to get to where you are, you can find the bearing to get you home

• This skill leads to angles in parallel lines
• This could help you if you want to work in engineering, design, arctitecture, the military, many branches of science, etc. Opticians use their understanding of angles to help people see better.

Preparing:

• Are you aware of what parallel and perpendicular lines are?
  

  What are perpendicular lines.ppt
  

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• Do we understand what is an angle? and do we know the vocabulary of angles?
  

  angle rules simple.pptx
  

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• You'll need to be able to do some simple arithmetic and it might help to have a calculator handy.
• You will have a deeper understanding if you also know what we mean by a proof.
• Try the true/false task to see how much you know.
  

  Angles_True_and_False_sorting_cards.docx
  

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Discovering:

• This section works best with Geogebra. You can download Geogebra here.

‍Angles at a point‍

• Let's explore this diagram:

• Here are three angles that meet at a point in the centre of a circle. What do they add up to?
• Try moving the points and changing the angles. What do you notice?

Angles at a point on a straight line

• Let's explore this diagram:

• Here are three angles that meet at a point on a straight line. What do they add up to?
• Try moving the points and changing the angles. What do you notice?

Vertically opposite angles in an X shape

• Let's explore this diagram:

• Here are the four angles that result from the intersection of two lines. What do you notice?
• Try moving the points and changing the angles. Is your rule still true?

Discussing:

• What is the size of the other orange angle? Why?
  Tell your learning partner. Convince them you're right. Show me on a mini whiteboard.

• What is the size of the blue angle at the top?
• What about the blue angle at the bottom?
  Show me on a mini whiteboard.
  
  
• How did you figure this out?
  Tell your learning partner. Convince them you're right. Write your method down for someone else to follow.
• Did your learning partner find the blue angles the same way you did?
  Be ready to explain your method to the rest of the class.
• If you've only found it one way so far, can you think of another way to be sure the blue angle is what you think it is?
  
  
• How could we adapt this idea to prove that vertically opposite angles are equal?

Modeling:

• Here are some examples of people getting it right:
• Watch out: some people get confused about angles on a straight line. What's wrong with this?

This is wrong. Why?

• Here are some more examples. Did they get it right or wrong? Explain how you know!

Explaining:

• One way to do this is...
• Another approach might be...
• A useful shortcut is to...
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practicing:

• Some straightforward examples.
• Some harder examples.
• Some mixed examples.
• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...